How Do Quantum Numbers Shape Atomic Structure?

In summary, the primary quantum number n determines the energy level of an electron, and the larger the value of n, the larger the angular momentum is permitted. The quantum number m represents the projection of the angular momentum on the z-axis and is quantized according to quantum mechanics. Differential equations play a crucial role in understanding the quantum model of the atom, as they are used to solve Schrödinger's equation and obtain the wave function of an electron. It is recommended to have a basic understanding of calculus before delving into this topic.
  • #1
cam875
228
0
im just learning the quantum model of the atom now and i have a few questions,

1st: why does the different energy levels represented by the primary quantum number n have different numbers of subshells represented by l such as 0,1,2,3. Energy level 1 can only have s or 0 but Energy Level 2 can have 0 or 1 which is s and p. Why is this, what is the difference between the two energy levels that causes this to be possible.

2nd: I don't understand what the m is for, it stands for magnetic or something but I am just confused about it, could someone explain that part of the 4 quantum numbers for describing an electron.

Thanks in advance.
 
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  • #2
i) It comes from the math, theory of differential equations, when you solve this Shcrödinger equation.

You can think "semiclassical" about this, n is the radial quantum number, and the larger it is, the larger angular momentum is permitted. (if we think of n as distance from centre). But the real answer is what you obtain when you solve the shcördinger equation.

Have you done class in partial differential equations? if not, maybe wait til then to try to get the solution buy yourself.

ii) m is the projection of l on the z-axis which is, according to QM, quantized.

http://en.wikipedia.org/wiki/Principal_quantum_number
http://en.wikipedia.org/wiki/Azimuthal_quantum_number
http://en.wikipedia.org/wiki/Magnetic_quantum_number
 
  • #3
no i have not done differential equations yet so yeah ill just wait for that, I am assuming that's where a lot of advanced physics equations are based around?
 
  • #4
yes, that is true. Knowing theory of differential equations, orthogonal functions etc. are essential for a physicsist
 
  • #5
cam875 said:
no i have not done differential equations yet so yeah ill just wait for that, I am assuming that's where a lot of advanced physics equations are based around?

Yes indeed. In mechanics, you solve Newton's Second Law as a differential equation for position as a function of time. In electricity & magnetism, Maxwell's equations are differential equations for the components of the electric and magnetic fields, as functions of position and time. In quantum mechanics, Schrödinger's equation is a differential equation for "psi" as a function of position versus time.

For QM, if you know basic calculus, you might try a second-year university "modern physics" textbook. They often introduce the concepts of differential equations specifically in connection with Schrödinger's equation, and show one or two simple solutions. For example, Beiser's "Concepts of Modern Physics." It has a chapter on the hydrogen atom, which gives the key steps and results from solving the SE for hydrogen, without going into all the mathematical details, which most students probably don't see until graduate school.
 
  • #6
ill be doing calculus next year so I am not jumping into this just yet :)
 

Related to How Do Quantum Numbers Shape Atomic Structure?

What is the quantum model of the atom?

The quantum model of the atom, also known as the quantum mechanical model, is a scientific theory that explains the behavior and structure of atoms at a subatomic level. It is based on the principles of quantum mechanics, which describe the behavior of particles on a very small scale.

How is the quantum model different from previous atomic models?

The quantum model differs from previous models, such as the Bohr model, in that it does not treat electrons as particles orbiting the nucleus in fixed paths. Instead, it describes the location of electrons in terms of probability clouds, where the electrons are most likely to be found at any given time.

What is an energy level in the quantum model?

An energy level in the quantum model refers to the specific amount of energy that an electron can have while orbiting the nucleus of an atom. These energy levels are quantized, meaning they only exist in specific, discrete values. When an electron absorbs or emits energy, it moves between these energy levels.

What is the Heisenberg uncertainty principle and how does it relate to the quantum model?

The Heisenberg uncertainty principle is a fundamental principle of quantum mechanics that states that it is impossible to know both the position and momentum of a particle at the same time. This relates to the quantum model as it explains the probabilistic nature of the location of electrons in an atom, as opposed to the definite paths described in classical mechanics.

How does the quantum model of the atom explain the periodic table?

The quantum model of the atom explains the periodic table by describing how electrons fill different energy levels and sublevels within an atom. This arrangement of electrons gives rise to the patterns and trends seen in the periodic table, such as the increasing number of protons and electrons as you move across a row, and the similar chemical properties of elements in the same column.

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